Prediction the Biodynamic Response of the Seated Human Body using Artificial Intelligence Technique

Mostafa A. M. Abdeen & W. Abbas
International Journal of Engineering (IJE), Volume (4): Issue (6) 491
Prediction the Biodynamic Response of the Seated Human Body
using Artificial Intelligence Technique
Mostafa A. M. Abdeen mostafa_a_m_abdeen@hotmail.com
Faculty of Engineering/Dept. of Engineering
Mathematics and Physics
Cairo University
Giza, 12211, Egypt
W. Abbas Wael_abass@hotmail.com
Eng. Physics and Mathematics Dept.,
Faculty of Eng. (Mataria)
Helwan University
Cairo, Egypt
Abstract
The biodynamic response behaviors of seated human body subject to whole-
body vibration have been widely investigated. The biodynamic response
characteristics of seated human subjects have been extensively reported in
terms of apparent mass and driving-point mechanical impedance while seat-to-
head vibration transmissibility has been widely used to characterize response
behavior of the seated subjects exposed to vibration. These functions (apparent
mass, driving-point mechanical impedance) describe “to-the-body” force–motion
relationship at the human–seat interface, while the transmissibility function
describes “through-the-body” vibration transmission properties. The current study
proposed a 4-DOF analytic biomechanical model of the human body in a sitting
posture without backrest in vertical vibration direction to investigate the
biodynamic responses of different masses and stiffness. Following the analytical
approach, numerical technique developed in the present paper to facilitate and
rapid the analysis. The numerical analysis used here applies one of the artificial
intelligence technique to simulate and predict the response behaviors of seated
human body for different masses and stiffness without the need to go through the
analytic solution every time. The Artificial Neural Network (ANN) technique is
introduced in the current study to predict the response behaviors for different
masses and stiffness rather than those used in the analytic solution. The results
of the numerical study showed that the ANN method with less effort was very
efficiently capable of simulating and predicting the response behaviors of seated
human body subject to whole-body vibration.
Keywords: Biodynamic Response, Analytic Seated Human Body Model, Numerical Simulation Model,
Artificial Neural Network.
1. INTRODUCTION
The biodynamic responses of seated human occupant exposed to vibration have been widely
characterized to define frequency-weightings for assessment of exposure, to identify human

sensitivity and perception of vibration, and to develop seated body models [1]. The biodynamic
response of the human body exposed to vibration have been invariably characterized through
measurement of force motion relationship at the point of entry of vibration ''To-the-body response
function'', expressed as the driving-point mechanical impedance (DPMI) or the apparent mass
(APMS) and transmission of vibration to different body segments ''Through-the-body response
function'', generally termed as seat-to-head transmissibility (STHT) for the seated occupant.
Considering that the human body is a complex biological system, the ''To-the-body'' response
function is conveniently characterized through non–invasive measurements at the driving point
alone.
The vast majority of the reported studies on biodynamic response to whole-body vibration have
considered vibration along the vertical axis alone. In many of the early studied, such as those
conducted by Coermann [2], Vogt [3], and Suggs [4], the numbers of subjects was usually
relatively small, and only sinusoidal excitation was used, not generally representative of the type
of excitation and levels of vibration usually encountered in practice. In many of these studies, the
feet of the subjects were either not supported or supported but not vibrated, a condition not
common in most driving situations. Fairley and Griffin [5], reported the vertical apparent mass of
60 seated subjects including men, women and children, which revealed a large scatter of data
presumably owing to large variations in the subject masses. Boileau et al. [6] investigated the
relationships between driving point mechanical impedance and seat-to-head transmissibility
functions based upon 11 reported one dimensional lumped parameter models. The majority of the
models showed differences in frequencies corresponding to peak magnitudes of the two
functions, which were expressed as resonant frequencies. Toward [7], summarized that a support
of the back caused higher resonance frequency and slightly lower peak magnitude of the APMS
response for subjects sitting on a horizontal plane. Wang et al. [8], study the vertical apparent
mass and seat-to-head transmissibility response characteristics of seated subjects are derived
through measurements of total biodynamic force at the seat pan, and motions of the seat pan and
head along the applied input acceleration direction, using 12 male subjects. The data were
acquired under three different back support conditions and two different hands positions
representative of drivers and passengers-like postures. Steina et al.[9], analyzed apparent mass
measurements in the y- direction with a group of 13 male test subjects exposed to three
excitation intensities.
In early studies, various biodynamic models have been developed to depict human motion from
single-DOF to multi-DOF models. These models can be divided as distributed (finite element)
models, lumped parameter models and multi-body models. The distributed model treats the spine
as a layered structure of rigid elements, representing the vertebral bodies, and deformable
elements representing the intervertebral discs by the finite element method. Multi-body human
models are made of several rigid bodies interconnected by pin (two-dimensional) or ball and
socket (three-dimensional) joints, and can be further separated into kinetic and kinematic models.
It is clear that the lumped-parameter model is probably one of the most popular analytical
methods in the study of biodynamic responses of seated human subjects, though it is limited to
one-directional analysis. However, vertical vibration exposure of the driver is our main concern.
Therefore, this paper carries out a thorough survey of literature on the lumped- parameter
models for seated human subjects exposed to vertical vibration.
The lumped parameter models consider the human body as several rigid bodies and spring-
dampers. This type of model is simple to analyze and easy to validate with experiments.
However, the disadvantage is the limitation to one-directional analysis. Coermann [2], measured
the driving-point impedance of the human body and suggested 1-DOF model. Suggs et al. [4],
developed a 2-DOF human body. It was modeled as a damped spring-mass system to build a
standardized vehicle seat testing procedure. A 3-DOF analytical model for a tractor seat
suspension system is presented by Tewari et al. [10]. It was observed that the model could be
employed as a tool in selection of optimal suspension parameters for any other type of vehicles.
Boileau et al. [11] used an optimization procedure to establish a 4-DOF human model based on
test data. It is quite clear from the literature mentioned previously the amount of effort

(experimentally or analytically) required to accurately investigate and understand the biodynamic
response behaviors of seated human body subject to whole-body vibration of different types and
magnitudes. This fact urged the need for utilizing new technology and techniques to facilitate this
comprehensive effort and at the same time preserving high accuracy.
Artificial intelligence has proven its capability in simulating and predicting the behavior of the
different physical phenomena in most of the engineering fields. Artificial Neural Network (ANN) is
one of the artificial intelligence techniques that have been incorporated in various scientific
disciplines. Ramanitharan and Li [12] utilized ANN with back-propagation algorithm for modeling
ocean curves that were presented by wave height and period. Abdeen [13] developed neural
network model for predicting flow depths and average flow velocities along the channel reach
when the geometrical properties of the channel cross sections were measured or vice versa.
Allam [14] used the artificial intelligence technique to predict the effect of tunnel construction on
nearby buildings which is the main factor in choosing the tunnel route. Allam, in her thesis,
predicted the maximum and minimum differential settlement necessary precautionary measures.
Azmathullah et al. [15] presented a study for estimating the scour characteristics downstream of a
ski-jump bucket using Neural Networks (NN). Abdeen [16] presented a study for the development
of ANN models to simulate flow behavior in open channel infested by submerged aquatic weeds.
Mohamed [17] proposed an artificial neural network for the selection of optimal lateral load-
resisting system for multi-story steel frames. Mohamed, in her master thesis, proposed the neural
network to reduce the computing time consumed in the design iterations. Abdeen [18] utilized
ANN technique for the development of various models to simulate the impacts of different
submerged weeds' densities, different flow discharges, and different distributaries operation
scheduling on the water surface profile in an experimental main open channel that supplies water
to different distributaries.
2. PROBLEM DESCRIPTION
To investigate the biodynamic response behaviors of seated human body subject to whole-body
vibration (sinusoidal wave with amplitude 5 m/s
2
), analytical and numerical techniques will be
presented in this study. The analytical model and its results will be described in detail in the
following sections. The numerical models presented in this study utilized Artificial Neural Network
technique (ANN) using the data and the results of the analytical model to understand the
biodynamic response behaviors and then can predict the behaviors for different data of the
human body without the need to go through the analytical solution.
3. ANALYTICAL MODEL
3.1 Biomechanical Modeling
The human body in a sitting posture can be modeled as a mechanical system that is composed of
several rigid bodies interconnected by springs and dampers. (Boileau, and Rakheja [11]). This
model as shown in Fig. 1 consists of four mass segments interconnected by four sets of springs
and dampers. The four masses represent the following four body segments: the head and neck
(m1), the chest and upper torso (m2), the lower torso (m3), and the thighs and pelvis in contact
with the seat (m4). The mass due to lower legs and the feet is not included in this representation,
assuming they have negligible contributions to the biodynamic response of the seated body. The
stiffness and damping properties of thighs and pelvis are (k4) and (c4), the lower torso are (k3) and
(c3), upper torso are (k2) and (c2), and head are (k1) and (c1).

FIGURE 1: Biomechanical Boileau and Rakheja 4-DOF model.
The equation of motion of the human body can be obtained as follows:
(1)
The system equations of motion, equation (1), for the model can be expressed in matrix form as
follows:
(2)
where , and are mass, damping, and stiffness matrices, respectively; is
the force vector due to external excitation.

And,
By taking the Fourier transformation of equation (2), the following matrix form of equation can be
obtained:
(3)
where, are the complex Fourier transformation vectors of
, respectively. ω is the excitation frequency. Vector contains complex
displacement responses of n mass segments as a function of ω
( ). consists of complex excitation forces
on the mass segments as a function of ω as well.
3.2 Biodynamic Response of Human Body
The biodynamic response of a seated human body exposed to whole-body vibration can be
broadly categorized into two types. The first category "To-the-body" force motion interrelation as
a function of frequency at the human-seat interface, expressed as the driving-point mechanical
impedance (DPMI) or the apparent mass (APMS). The second category "Through-the-body"
response function, generally termed as seat-to-head transmissibility (STHT) for the seated
occupant.
The DPMI relates the driving force and resulting velocity response at the driving point (the seat-
buttocks interface), and is given by [1]:
(4)
where, is the complex DPMI, and or ( ) are the driving force and
response velocity at the driving point, respectively. is the angular frequency in rad/s , and j
= is the complex phasor.
Accordingly, DPMI for the model can be represented as:
(5)
In a similar manner, the apparent mass response relates the driving force to the resulting
acceleration response, and is given by [19]:
(6)
where, is the acceleration response at the driving point.
The magnitude of APMS offers a simple physical interpretation as it is equal to the static mass of
the human body supported by the seat at very low frequencies, when the human body resembles
that of a rigid mass. The above two functions are frequently used interchangeably, due to their
direct relationship that given by:

(7)
APMS for the model can be represented as:
(8)
The biodynamic response characteristics of seated occupants exposed to whole body vibration
can also be expressed in terms of seat-to-head transmissibility (STHT), which is termed as
"through-the-body" response function. Unlike the force-motion relationship at the driving-point, the
STHT function describes the transmission of vibration through the seated body. The STHT
response function is expressed as:
(9)
where, is the complex STHT, is the response acceleration measured at the
head of seated occupant, and is the acceleration response at the driving point. According
to equation (9) seat-to-head transmissibility for the model is:
(10)
The above three functions have been widely used to characterize the biodynamic responses of
the seated human subjects exposed to whole body vibration.
4. ANALYTIC RESULTS AND DISCUSSIONS
On the basis of anthropometric Boileau data [19], the proportion of total body weight estimated for
different body segments is 7.5% for the head and neck, 40.2% for the chest and upper torso,
12.2% for the lower torso, and 18.2% for the thighs and upper legs. For a seated driver with mean
body mass, maintaining an erect back not supported posture, 78% of the weight was found to be
supported by the seat. The biomechanical parameters of the human model (Stiffness, Damping)
are listed in Table 1.
Stiffness Coefficient
(N/m)
Damping coefficient
(N.s/m)
k1 = 310000 c1 = 400
k2 = 183000 c2 = 4750
k3 = 162800 c3 = 4585
k4 = 90000 c4 = 2064
TABLE 1: The biomechanical parameters of the Boileau and Rakheja model.
4.1 Response Behaviors of the Human Body
In the following subsections the effect of body's mass, stiffness coefficient, and damping
coefficient on the response behaviors of the human body (STHT, DPMI, and APMS) will be
investigated using the analytical solution presented in the current study.
4.1.1 Effect of Human Body’s Mass
Three different total body masses (65, 75, and 85 kg) are used to investigate the effect of mass
on the response behaviors of human body (STHT, DPMI and APMS) as shown in Fig. 2 (a, b, and
c) respectively. From these figures, one can see that by increasing the human body mass, the
biodynamic response characteristics of seated human body (STHT, DPMI, and APMS) are
increased.

0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
Seat-to-headTransmissibility
: 65Kg
: 75Kg
: 85Kg
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency (Hz)Driving-pointmechanicalimpedance
: 65Kg
: 75Kg
: 85Kg
0 5 10 15 20
0
20
40
60
80
100
120
Frequency(Hz)
Apparentmass
: 65Kg
: 75Kg
: 85Kg
0 5 10 15 20
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Apparentmass
:k4=90000
:k4=90000 +40%
:k4=90000 - 40%
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency(Hz)
Driving-pointmechanicalimpedance
:k4=90000
:k4=90000 + 40%
:k4=90000 - 40%
0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
:k4=90000
:k4=90000 + 40%
:k4=90000 - 40%
(a) (b) (c)
FIGURE 2: Effect of human body’s mass on the biodynamic response behavior (Analytic Results)((a) STHT,
(b) DPMI and (c) APMS).
4.1.2 Effect of Stiffness Coefficient
Three different values of pelvic stiffness k4 (Boileau value (B.V.), B.V. +40%, and B.V. -40%) are
used to investigate the effect of pelvic stiffness on the response behaviors of human body (STHT,
DPMI and APMS) as shown in Fig. 3 (a, b, and c) respectively. From these figures, it is clear that
by increasing the pelvic stiffness, the biodynamic response characteristics of seated human body
(STHT, DPMI, and APMS) are increased.
(a) (b) (c)
FIGURE 3: Effect of stiffness coefficient on the biodynamic response behaviors (Analytic Results) ((a)
STHT, (b) DPMI and (c) APMS).
4.1.3 Effect of Damping Coefficient
Three different values of pelvic damping coefficient C4 (Boileau value (B.V.), B.V. +40%, and B.V.
-40%) are used to investigate the effect of pelvic damping coefficient on the response behaviors
of human body (STHT, DPMI and APMS) as shown in Fig. 4 (a, b, and c) respectively. From
these figures, it is clear that by increasing pelvic damping coefficient, the biodynamic response
characteristics of seated human body (STHT, DPMI, and APMS) are decreased.

0 5 10 15 20
0
20
40
60
80
100
120
140
160
180
Frequency(Hz)
Apparentmass
:C4=2064
:C4=2064 + 40%
:C4=2064 - 40%
0 2 4 6 8 10 12 14 16 18 20
0
1000
2000
3000
4000
5000
6000
Frequency(Hz)
:C4=2064
:C4=2064 + 40%
:C4=2064 - 40%
0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Frequency (Hz)
:C4=2064
:C4=2064 + 40%
:C4=2064 - 40%
(a) (b) (c)
FIGURE 4: Effect of damping coefficient on the biodynamic response behaviors (Analytic Results)
((a) STHT, (b) DPMI and (c) APMS)
5. NUMERICAL MODEL STRUCTURE
Neural networks are models of biological neural structures. Abdeen [13] described in a very
detailed fashion the structure of any neural network. Briefly, the starting point for most networks is
a model neuron as shown in Fig. (5). This neuron is connected to multiple inputs and produces a
single output. Each input is modified by a weighting value (w). The neuron will combine these
weighted inputs with reference to a threshold value and an activation function, will determine its
output. This behavior follows closely the real neurons work of the human’s brain. In the network
structure, the input layer is considered a distributor of the signals from the external world while
hidden layers are considered to be feature detectors of such signals. On the other hand, the
output layer is considered as a collector of the features detected and the producer of the
response.
FIGURE 5: Typical picture of a model neuron that exists in every neural network
5.1 Neural Network Operation
It is quite important for the reader to understand how the neural network operates to simulate
different physical problems. The output of each neuron is a function of its inputs (Xi). In more
details, the output (Yj) of the j
th
neuron in any layer is described by two sets of equations as
follows:

∑ 




=
ij
w
i
XjU (11)
And
( )jtjUthFjY += (12)
For every neuron, j, in a layer, each of the i inputs, Xi, to that layer is multiplied by a previously
established weight, wij. These are all summed together, resulting in the internal value of this
operation, Uj. This value is then biased by a previously established threshold value, tj, and sent
through an activation function, Fth. This activation function can take several forms such as Step,
Linear, Sigmoid, Hyperbolic, and Gaussian functions. The Hyperbolic function, used in this study,
is shaped exactly as the Sigmoid one with the same mathematical representation, as in equation
3, but it ranges from – 1 to + 1 rather than from 0 to 1 as in the Sigmoid one (Fig. 6)
( ) xe
xf −+
=
1
1
(13)
The resulting output, Yj, is an input to the next layer or it is a response of the neural network if it is
the last layer. In applying the Neural Network technique, in this study, Neuralyst Software, Shin
[20], was used.
FIGURE 6: The Sigmoid Activation Function
5.2 Neural Network Training
The next step in neural network procedure is the training operation. The main purpose of this
operation is to tune up the network to what it should produce as a response. From the difference
between the desired response and the actual response, the error is determined and a portion of it
is back propagated through the network. At each neuron in the network, the error is used to
adjust the weights and the threshold value of this neuron. Consequently, the error in the network
will be less for the same inputs at the next iteration. This corrective procedure is applied
continuously and repetitively for each set of inputs and corresponding set of outputs. This
procedure will decrease the individual or total error in the responses to reach a desired tolerance.
Once the network reduces the total error to the satisfactory limit, the training process may stop.
The error propagation in the network starts at the output layer with the following equations:
( )ijijij XeLRww += '
(14)
And,
( )( )jYjdjYjYje −−= 1 (15)

Where, wij is the corrected weight, w’
ij is the previous weight value, LR is the learning rate, ej is
the error term, Xi is the ith
input value, Yj is the output, and dj is the desired output.
6. NUMERICAL SIMULATION CASES
To fully investigate numerically the biodynamic response behaviors of seated human body
subject to whole body vibration, several simulation cases are considered in this study. These
simulation cases can be divided into two groups to simulate the response behaviors due to
changing of human body’s mass and stiffness respectively. From the analytic investigation, it is
clear that the effect of damping coefficient is opposite to the effect of stiffness coefficient on the
response behaviors of the human body. So in the numerical analysis, the effect of stiffness
coefficient will be studied only in addition with the effect of human body’s mass.
6.1 Neural Network Design
To develop a neural network model to simulate the effect of mass and stiffness on the biodynamic
response behaviors of seated human body, first input and output variables have to be
determined. Input variables are chosen according to the nature of the problem and the type of
data that would be collected. To clearly specify the key input variables for each neural network
simulation group and their associated outputs, Tables 2 and 3 are designed to summarize all
neural network key input and output variables for the first and second simulation groups
respectively.
It can be noticed from Tables 2 and 3 that every simulation group consists of three simulation
cases (three neural network models) to study the effect of mass and stiffness on the seat-to-head
transmissibility (STHT), driving point mechanical impedance (DPMI) and apparent mass (APMS).
Simulation
Case
Input Variables Output
STHT
m1 m2 m3 m4 Frequency
STHT
DPMI DPMI
APMS APMS
TABLE 2: Key input and output variables for the first neural network simulation group (effect of human
body’s mass)
Simulation
Case
Input Variables Output
STHT
k4 Frequency
STHT
DPMI DPMI
APMS APMS
TABLE 3: Key input and output variables for the second neural network simulation group (effect of stiffness
coefficient)
Several neural network architectures are designed and tested for all simulation cases
investigated in this study to finally determine the best network models to simulate, very
accurately, the effect of mass and stiffness based on minimizing the Root Mean Square Error
(RMS-Error). Fig. 7 shows a schematic diagram for a generic neural network. The training
procedure for the developed ANN models, in the current study, uses the data from the results of
the analytical model to let the ANN understands the behaviors. After sitting finally the ANN
models, these models are used to predict the biodynamic response behaviors for different
masses and stiffness rather than those used in the analytic solution.

Table 4 shows the final neural network models for the two simulation groups and their associate
number of neurons. The input and output layers represent the key input and output variables
described previously for each simulation group.
FIGURE 7: General schematic diagram of a simple generic neural network
Simulation Group
No. of
Layers
No. of Neurons in each Layer
Input
Layer
First
Hidden
Second
Hidden
Third
Hidden
Output
Layer
First
Group
(mass)
STHT 5 5 6 4 2 1
DPMI
4 5 6 4 - 1
APMS
Second
Group
(Stiffness)
STHT
4 2 5 3 - 1DPMI
APMS
TABLE 4: The developed neural network models for all the simulation cases
The parameters of the various network models developed in the current study for the different
simulation models are presented in table 5. These parameters can be described with their tasks
as follows:
Learning Rate (LR): determines the magnitude of the correction term applied to adjust each
neuron’s weights during training process = 1 in the current study.
Momentum (M): determines the “life time” of a correction term as the training process takes
place = 0.9 in the current study.
Training Tolerance (TRT): defines the percentage error allowed in comparing the neural
network output to the target value to be scored as “Right” during the training process = 0.001 in
the current study.
Testing Tolerance (TST): it is similar to Training Tolerance, but it is applied to the neural
network outputs and the target values only for the test data = 0.003 in the current study.
Input Noise (IN): provides a slight random variation to each input value for every training epoch
= 0 in the current study.
Hidden layer
3 neurons
Hidden layer
3 neurons
Output # 2
Input # 1 Output # 1
Input # 2

Function Gain (FG): allows a change in the scaling or width of the selected function = 1 in the
current study.
Scaling Margin (SM): adds additional headroom, as a percentage of range, to the rescaling
computations used by Neuralyst Software, Shin (1994), in preparing data for the neural network
or interpreting data from the neural network = 0.1 in the current study.
Training Epochs: number of trails to achieve the present accuracy.
Percentage Relative Error (PRR): percentage relative error between the numerical results and
actual measured value and is computed according to equation (16) as follows:
PRE = (Absolute Value (ANN_PR - AMV)/AMV)*100 (16)
Where :
ANN_PR : Predicted results using the developed ANN model
AMV : Actual Measured Value
MPRE: Maximum percentage relative error during the model results for the training step.
Simulation Group
Training
Epochs
MPRE RMS-Error
First
Group
(mass)
STHT 45931 1.213 0.0015
DPMI 7560 2.609 0.0022
APMS 7174 3.743 0.0023
Second
Group
(Stiffness)
STHT 14012 3.449 0.0014
DPMI 100185 3.938 0.002
APMS 101463 1.644 0.0012
TABLE 5: Parameters used in the developed neural network models
7. NUEMERICAL RESULTS AND DISCUSSIONS
Numerical results using ANN technique will be presented in this section for the two groups (six
models) to show the simulation and prediction powers of ANN technique for the effect of human
body’s mass and stiffness coefficient on the biodynamic response behaviors (STHT, DPMI and
APMS) subject to whole-body vibration.
7.1 Effect of human body’s mass
Three ANN models are developed to simulate and predict the effect of human body’s mass on the
biodynamic response behaviors (STHT, DPMI and APMS). Figures 8, 9, and 10 show the ANN
results and analytical ones for different human body’s masses. From ANN training figures (Left), it
is very clear that ANN understands and simulates very well the biodynamic response behaviors.
After that the developed ANN models used very successfully and efficiently to predict the
response behaviors for different masses rather than those used in the analytic solution as shown
in the predicted figures of ANN results (Right).

0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
Seat-to-headTransmissibility :Analytical 65Kg
:ANN Training 65Kg
:Analytical 75Kg
:ANN Training 75Kg
:Analytical 85Kg
:ANN Training 85Kg
0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
:ANN Predicted 60Kg
:Analytical 65Kg
:ANN Predicted 80Kg
:Analytical 85Kg
:ANN Predicted 90Kg
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency (Hz)
:Analytical 65Kg
:ANN Training 65Kg
:Analytical 75Kg
:ANN Training 75Kg
:Analytical 85Kg
:ANN Training 85Kg
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency (Hz)
:ANN Predicted 60Kg
:Analytical 65Kg
:ANN Predicted 80Kg
:Analytical 85Kg
:ANN Predicted 90Kg
0 5 10 15 20
0
20
40
60
80
100
120
Frequency (Hz)
Apparentmass
:Analytical 65Kg
:ANN Training 65Kg
:Analytical 75Kg
:ANN Training 75Kg
:Analytical 85Kg
:ANN Training 85Kg
0 5 10 15 20
0
20
40
60
80
100
120
Frequency (Hz)
Apparentmass
:ANN Predicted 60Kg
:Analytical 65Kg
:ANN Predicted 80Kg
:Analytical 85Kg
:ANN Predicted 90Kg
FIGURE 8: ANN results for the effect of human body’s mass on STHT
(Left : ANN Training, Right : ANN Prediction)
FIGURE 9: ANN results for the effect of human body’s mass on DPMI
FIGURE 10: ANN results for the effect of human body’s mass on APMS

0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
:Analytical at k4= 90000+40%
:ANN Training at k4= 90000+40%
:Analytical at k4=90000
:ANN Training at k4=90000
:Analytical at k4= 90000-40%
:ANN Training at k4= 90000-40%
0 5 10 15 20
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Frequency (Hz)
:ANN Predicted at k4=90000+60%
:Analytical at k4=90000+40%
:ANN Predicted at k4=90000+20%
:Analytical at k4=90000-40%
:ANN Predicted at k4=90000-20%
:ANN Predicted at k4=90000-60%
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency (Hz)
:ANN Predicted at K4=90000+60%
:Analytical at K4=90000+40%
:ANN Predicted at K4=90000+20%
:Analytical at k4=90000-40%
:ANN Predicted at K4=90000-20%
:ANN Predicted at K4= 90000-60%
0 5 10 15 20
0
500
1000
1500
2000
2500
3000
3500
Frequency (Hz)
:Analytical at K4= 90000+40%
:ANN Training at K4= 90000+40%
:Analytical at K4= 90000
:ANN Training at K4= 90000
:Analytical at K4= 90000-40%
:ANN Training at K4= 90000-40%
7.2 Effect of stiffness coefficient
Another three ANN models are developed in this sub-section to simulate and predict the effect of
stiffness coefficient (k4) on the biodynamic response behaviors (STHT, DPMI and APMS).
Figures 11, 12, and 13 show the ANN results and analytical ones for different values of k4. From
ANN training figures (Left), it is very clear that ANN understands and simulates very well the
biodynamic response behaviors. After that the developed ANN models used very successfully
and efficiently to predict the response behaviors for different values of k4 rather than those used
in the analytic solution as shown in the predicted figures of ANN results(Right).
FIGURE 11: ANN results for the effect stiffness coefficient on STHT
FIGURE12: ANN results for the effect stiffness coefficient on DPMI

0 5 10 15 20
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Apparentmass
:ANN Predicted at K4= 90000+60%
:ANN Predicted at K4= 90000+20%
:Analytical at K4= 90000-40%
0 5 10 15 20
10
20
30
40
50
60
70
80
90
Frequency (Hz)
Apparentmass
:ANN Training at K4= 90000+40%
:Analytical at K4= 90000
:ANN Training at K4= 90000
:Analytical at k4= 90000-40%
:ANN Training at k4= 90000-40%
FIGURE 13: ANN results for the effect stiffness coefficient on APMS
8. CONCLUSIONS
Based on the analytical investigation conducted in the course of the current research, it could be
concluded that the change in human body's mass, pelvic stiffness, and pelvic damping coefficient
give a remarkable change in biodynamic response behaviors of seated human body (direct
proportional for human body’s mass and pelvic stiffness coefficient and inverse proportional for
pelvic damping coefficient.)
Based on the results of implementing the ANN technique in this study, the following can be
concluded:
1. The developed ANN models presented in this study are very successful in simulating the
effect of human body’s mass and stiffness on the biodynamic response behaviors under
whole-body vibration.
2. The presented ANN models are very efficiently capable of predicting the response behaviors
at different masses and stiffness rather than those used in the analytic solution.
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vibration’’ Journal of Biomechanics Vol. 22, No 2, PP. 81–94, 1989.
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of holding a steering wheel’’, In Proceedings of the 39th United Kingdom Group, Meeting
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building adjacent to Tunnel Rout during Tunneling Process” Ph.D., 2005.
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Scour Downstream of a Ski-Jump Bucket", Journal of Hydrologic Engineering, ASCE, Vol.
131, Issue 10, pp. 898-908, 2005.
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Behavior in Open Channel Infested by Submerged Aquatic Weeds”, Journal of Mechanical
Science and Technology, KSME Int. J., Vol. 20, No. 10, Soul, Korea, 2006
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